Paper Citation Record · LEDGER

HTMuon: Improving Muon via Heavy-Tailed Spectral Correction

As of 5 August 2026, this Paper Citation Record lists 44 of 44 outbound references and 6 inbound Pith citation observations for arXiv:2603.10067.

A citation records a reference. It does not transfer a finding from one paper to another.

pith.paper-citation-record.v1
2603.10067 v2

Coverage vector

measured 44 of 44 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-05-25T06:50:29.893126Z

measured 50 of 50 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-05T06:32:48.257954+00:00

measured 6 of 6 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links, observed 2026-08-04T04:19:39.069342Z

measured 0 of 1 external citation measurements

A source-named dated measurement, never combined with another source.

Source: pith, observed 2026-06-30T18:35:00.450797Z

Reference resolution

44 of 44 outbound references displayed

verified exact37
verified fuzzy6
unresolved1
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External citation measurements

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Outbound references

Observation f9c45aab-3c14-4310-8aea-872a5b89da6f · outbound

This paper cites Modular Duality in Deep Learning.

HTMuon: Improving Muon via Heavy-Tailed Spectral Correction Modular Duality in Deep Learning

Reference 1

Resolution: verified exact; arxiv_id, observed 2026-05-25T06:55:26.275684Z

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Observation ccd6c3b7-6307-4ad8-9bd9-a6ab2a01ef71 · outbound

This paper cites On the Convergence of Muon and Beyond.

HTMuon: Improving Muon via Heavy-Tailed Spectral Correction On the Convergence of Muon and Beyond

Reference 2

Resolution: verified exact; local_arxiv, observed 2026-05-25T06:55:26.395118Z

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Observation 7beef605-7f0e-43fb-b41b-a53885468d96 · outbound

This paper cites Distributional Associations vs In-Context Reasoning: A Study of Feed-forward and Attention Layers.

HTMuon: Improving Muon via Heavy-Tailed Spectral Correction Distributional Associations vs In-Context Reasoning: A Study of Feed-forward and Attention Layers

Reference 3

Resolution: verified exact; arxiv_id, observed 2026-05-25T06:55:26.332463Z

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Observation 15e8daa2-7fef-4f00-bad4-7bc528dae251 · outbound

This paper cites Muon optimizes under spectral norm constraints.arXiv preprint arXiv:2506.15054.

HTMuon: Improving Muon via Heavy-Tailed Spectral Correction Muon optimizes under spectral norm constraints.arXiv preprint arXiv:2506.15054

Reference 4

Resolution: verified exact; arxiv_id, observed 2026-05-25T06:55:26.321321Z

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Observation 0c29e495-9240-4578-8749-506342fb3e01 · outbound

This paper cites A Random Matrix Theory Perspective on the Spectrum of Learned Features and Asymptotic Generalization Capabilities.

HTMuon: Improving Muon via Heavy-Tailed Spectral Correction A Random Matrix Theory Perspective on the Spectrum of Learned Features and Asymptotic Generalization Capabilities

Reference 5

Resolution: verified exact; arxiv_id, observed 2026-05-25T06:55:26.372607Z

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Observation 92160a57-070a-406a-aa9c-b247e01ad884 · outbound

This paper cites When do spectral gradient updates help in deep learning?arXiv preprint arXiv:2512.04299.

HTMuon: Improving Muon via Heavy-Tailed Spectral Correction When do spectral gradient updates help in deep learning?arXiv preprint arXiv:2512.04299

Reference 6

Resolution: verified exact; arxiv_id, observed 2026-05-25T06:55:26.417239Z

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Observation a8f52aed-42e7-441c-b164-d34bf66ab658 · outbound

This paper cites Scaling Laws and Spectra of Shallow Neural Networks in the Feature Learning Regime.

HTMuon: Improving Muon via Heavy-Tailed Spectral Correction Scaling Laws and Spectra of Shallow Neural Networks in the Feature Learning Regime

Reference 7

Resolution: verified exact; arxiv_id, observed 2026-06-05T02:16:19.798327Z

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Observation 06230e85-42e7-4175-a745-512a5f804f9a · outbound

This paper cites An Image is Worth 16x16 Words: Transformers for Image Recognition at Scale.

HTMuon: Improving Muon via Heavy-Tailed Spectral Correction An Image is Worth 16x16 Words: Transformers for Image Recognition at Scale

Reference 8

Resolution: verified exact; local_arxiv, observed 2026-05-25T06:55:26.315204Z

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Observation aacdf1e9-ef87-4a6e-bda6-82d64af8c54c · outbound

This paper cites Sharpness-Aware Minimization for Efficiently Improving Generalization.

HTMuon: Improving Muon via Heavy-Tailed Spectral Correction Sharpness-Aware Minimization for Efficiently Improving Generalization

Reference 9

Resolution: verified exact; local_arxiv, observed 2026-05-25T06:55:26.345190Z

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Observation 8f298c13-e139-4fd0-9323-925cda206988 · outbound

This paper cites Handbook of Convergence Theorems for (Stochastic) Gradient Methods.

HTMuon: Improving Muon via Heavy-Tailed Spectral Correction Handbook of Convergence Theorems for (Stochastic) Gradient Methods

Reference 10

Resolution: verified exact; arxiv_id, observed 2026-05-25T06:55:26.291179Z

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Observation ec108544-ba1a-4ec2-a5aa-604cd9576be6 · outbound

This paper cites Alphadecay: Module-wise weight decay for heavy-tailed balancing in llms.arXiv preprint arXiv:2506.14562.

HTMuon: Improving Muon via Heavy-Tailed Spectral Correction Alphadecay: Module-wise weight decay for heavy-tailed balancing in llms.arXiv preprint arXiv:2506.14562

Reference 11

Resolution: verified exact; arxiv_id, observed 2026-05-25T06:55:26.390965Z

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Observation 9d9e2f27-44b8-4182-b310-ab55e6f98f05 · outbound

This paper cites Models of Heavy-Tailed Mechanistic Universality.

HTMuon: Improving Muon via Heavy-Tailed Spectral Correction Models of Heavy-Tailed Mechanistic Universality

Reference 12

Resolution: verified exact; arxiv_id, observed 2026-05-25T06:55:26.285947Z

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Observation 4a86a8f2-8989-4e2a-91af-c5a8ba3722fa · outbound

This paper cites Adam: A Method for Stochastic Optimization.

HTMuon: Improving Muon via Heavy-Tailed Spectral Correction Adam: A Method for Stochastic Optimization

Reference 13

Resolution: verified exact; local_arxiv, observed 2026-05-25T06:55:26.256135Z

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Observation e6395f02-e157-46bf-891b-62764c654a99 · outbound

This paper cites Normuon: Making muon more efficient and scalable.arXiv preprint arXiv:2510.05491.

HTMuon: Improving Muon via Heavy-Tailed Spectral Correction Normuon: Making muon more efficient and scalable.arXiv preprint arXiv:2510.05491

Reference 14

Resolution: verified exact; arxiv_id, observed 2026-05-25T06:55:26.341475Z

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Observation bda48bfa-1f80-45e6-a818-9d4183666430 · outbound

This paper cites Cautious optimizers: Improving training with one line of code.arXiv preprint arXiv:2411.16085.

HTMuon: Improving Muon via Heavy-Tailed Spectral Correction Cautious optimizers: Improving training with one line of code.arXiv preprint arXiv:2411.16085

Reference 15

Resolution: verified exact; arxiv_id, observed 2026-05-25T06:55:26.350568Z

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Observation f65aeb92-3dfa-4e91-9a24-53946232c73b · outbound

This paper cites Sophia: A Scalable Stochastic Second-order Optimizer for Language Model Pre-training.

HTMuon: Improving Muon via Heavy-Tailed Spectral Correction Sophia: A Scalable Stochastic Second-order Optimizer for Language Model Pre-training

Reference 16

Resolution: verified exact; arxiv_id, observed 2026-05-25T06:55:26.310837Z

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Observation aeb40549-59d0-4f8b-9174-b36fa81f8d43 · outbound

This paper cites Charles H Martin and Christopher Hinrichs.

HTMuon: Improving Muon via Heavy-Tailed Spectral Correction Charles H Martin and Christopher Hinrichs

Reference 17

Resolution: verified exact; arxiv_id, observed 2026-05-25T06:55:26.377465Z

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Observation 4693facf-b701-40fa-bd46-fa0b3bf39304 · outbound

This paper cites Spectral Normalization for Generative Adversarial Networks.

HTMuon: Improving Muon via Heavy-Tailed Spectral Correction Spectral Normalization for Generative Adversarial Networks

Reference 18

Resolution: verified exact; local_arxiv, observed 2026-05-25T06:55:26.301348Z

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Observation df21e82d-6067-4255-b756-bca33ec8d6b7 · outbound

This paper cites 2 OLMo 2 Furious.

HTMuon: Improving Muon via Heavy-Tailed Spectral Correction 2 OLMo 2 Furious

Reference 19

Resolution: verified exact; local_arxiv, observed 2026-05-25T06:55:26.358590Z

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Observation f5598fc2-90df-4160-9a29-fdd841dfd058 · outbound

This paper cites Training Deep Learning Models with Norm-Constrained LMOs.

HTMuon: Improving Muon via Heavy-Tailed Spectral Correction Training Deep Learning Models with Norm-Constrained LMOs

Reference 20

Resolution: verified exact; local_arxiv, observed 2026-05-25T06:55:26.399470Z

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Observation bd78ae6a-878b-48cd-961f-806021dbee74 · outbound

This paper cites Benchmarking Optimizers for Large Language Model Pretraining.

HTMuon: Improving Muon via Heavy-Tailed Spectral Correction Benchmarking Optimizers for Large Language Model Pretraining

Reference 21

Resolution: verified exact; arxiv_id, observed 2026-05-25T06:55:26.265757Z

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Observation 6d9c33b0-99ee-4795-8c89-42204078306f · outbound

This paper cites Practical Efficiency of Muon for Pretraining.

HTMuon: Improving Muon via Heavy-Tailed Spectral Correction Practical Efficiency of Muon for Pretraining

Reference 22

Resolution: verified exact; arxiv_id, observed 2026-05-25T06:55:26.326911Z

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Observation 160edf2d-14ab-4677-931e-5f21e2af6606 · outbound

This paper cites The Truth is in There: Improving Reasoning in Language Models with Layer-Selective Rank Reduction.

HTMuon: Improving Muon via Heavy-Tailed Spectral Correction The Truth is in There: Improving Reasoning in Language Models with Layer-Selective Rank Reduction

Reference 23

Resolution: verified exact; arxiv_id, observed 2026-05-25T06:55:26.261039Z

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Observation 6ed23634-38dc-419f-901c-9abef5858ed5 · outbound

This paper cites On the Convergence Analysis of Muon.

HTMuon: Improving Muon via Heavy-Tailed Spectral Correction On the Convergence Analysis of Muon

Reference 24

Resolution: verified exact; local_arxiv, observed 2026-05-25T06:55:26.408057Z

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Observation 02e03c14-6266-4f5a-8ebe-954b2957cc61 · outbound

This paper cites Adamuon: Adaptive muon optimizer.arXiv preprint arXiv:2507.11005.

HTMuon: Improving Muon via Heavy-Tailed Spectral Correction Adamuon: Adaptive muon optimizer.arXiv preprint arXiv:2507.11005

Reference 25

Resolution: verified exact; arxiv_id, observed 2026-05-25T06:55:26.306017Z

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Observation 475a2365-f723-4772-934e-c7e9760926d2 · outbound

This paper cites Kimi K2: Open Agentic Intelligence.

HTMuon: Improving Muon via Heavy-Tailed Spectral Correction Kimi K2: Open Agentic Intelligence

Reference 26

Resolution: verified exact; local_arxiv, observed 2026-05-25T06:55:26.270032Z

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Observation 649ed638-4630-4f02-83c0-a921fd26226e · outbound

This paper cites LLaMA: Open and Efficient Foundation Language Models.

HTMuon: Improving Muon via Heavy-Tailed Spectral Correction LLaMA: Open and Efficient Foundation Language Models

Reference 27

Resolution: verified exact; local_arxiv, observed 2026-05-25T06:55:26.386042Z

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Observation 99cc1c97-1e58-40d7-bfd1-e3ae61c35ddb · outbound

This paper cites SOAP: Improving and Stabilizing Shampoo using Adam.

HTMuon: Improving Muon via Heavy-Tailed Spectral Correction SOAP: Improving and Stabilizing Shampoo using Adam

Reference 28

Resolution: verified exact; local_arxiv, observed 2026-05-25T06:55:26.280782Z

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Observation a360dbec-4d41-4696-b2de-eebb94653473 · outbound

This paper cites The Sharpness Disparity Principle in Transformers for Accelerating Language Model Pre-Training.

HTMuon: Improving Muon via Heavy-Tailed Spectral Correction The Sharpness Disparity Principle in Transformers for Accelerating Language Model Pre-Training

Reference 29

Resolution: verified exact; arxiv_id, observed 2026-05-25T06:55:26.251896Z

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Observation 45c9cbeb-8e58-40d2-a287-70f50c676984 · outbound

This paper cites Fantastic Pretraining Optimizers and Where to Find Them.

HTMuon: Improving Muon via Heavy-Tailed Spectral Correction Fantastic Pretraining Optimizers and Where to Find Them

Reference 30

Resolution: verified exact; arxiv_id, observed 2026-05-25T06:55:26.412629Z

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Observation a767a7f1-1c97-42be-904b-2253a4f48c5c · outbound

This paper cites MARS: Unleashing the Power of Variance Reduction for Training Large Models.

HTMuon: Improving Muon via Heavy-Tailed Spectral Correction MARS: Unleashing the Power of Variance Reduction for Training Large Models

Reference 31

Resolution: verified exact; arxiv_id, observed 2026-05-25T06:55:26.336736Z

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Observation 19aad6c9-5e71-47a6-94d0-be3159743578 · outbound

This paper cites GLM-4.5: Agentic, Reasoning, and Coding (ARC) Foundation Models.

HTMuon: Improving Muon via Heavy-Tailed Spectral Correction GLM-4.5: Agentic, Reasoning, and Coding (ARC) Foundation Models

Reference 32

Resolution: verified exact; local_arxiv, observed 2026-05-25T06:55:26.382052Z

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Observation e5a3fabf-f38c-4e64-9ac4-d0c20c0a182e · outbound

This paper cites Adam-mini: Use Fewer Learning Rates To Gain More.

HTMuon: Improving Muon via Heavy-Tailed Spectral Correction Adam-mini: Use Fewer Learning Rates To Gain More

Reference 33

Resolution: verified exact; arxiv_id, observed 2026-05-25T06:55:26.368446Z

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Observation fc8dac07-cfcb-470c-a35b-d843a4e5a483 · outbound

This paper cites GaLore: Memory-Efficient LLM Training by Gradient Low-Rank Projection.

HTMuon: Improving Muon via Heavy-Tailed Spectral Correction GaLore: Memory-Efficient LLM Training by Gradient Low-Rank Projection

Reference 34

Resolution: verified exact; local_arxiv, observed 2026-05-25T06:55:26.403505Z

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Observation f0a8c1cc-8184-48cb-8307-28236562e561 · outbound

This paper cites an unresolved cited work.

HTMuon: Improving Muon via Heavy-Tailed Spectral Correction Unresolved cited work

Reference 35

Resolution: unresolved; raw_fallback, observed 2026-05-25T07:16:43.581813Z

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Observation b7a17725-972c-4201-a764-4466462933c5 · outbound

This paper cites (2023); Garrigos and Gower (2023).

HTMuon: Improving Muon via Heavy-Tailed Spectral Correction (2023); Garrigos and Gower (2023)

Reference 36

Resolution: verified fuzzy; raw_fallback, observed 2026-05-25T07:16:43.584965Z

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Observation faddeed0-19ac-4602-bcc3-35291a23e60b · outbound

This paper cites Learning rate for both models and optimizers is 0.03.

HTMuon: Improving Muon via Heavy-Tailed Spectral Correction Learning rate for both models and optimizers is 0.03

Reference 37

Resolution: verified exact; arxiv_id, observed 2026-05-25T06:55:26.421929Z

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Observation 824f9f6d-ddba-4cfa-af30-5f0db34df80d · outbound

This paper cites For example, COSMOS outperforms Muon by 0.15 PPL for LLaMA-135M in (Liu et al., 2025b) and AlphaDecay outperforms Adam by 0.11 PPL for LLaMA-1B in (He et al., 2025).

HTMuon: Improving Muon via Heavy-Tailed Spectral Correction For example, COSMOS outperforms Muon by 0.15 PPL for LLaMA-135M in (Liu et al., 2025b) and AlphaDecay outperforms Adam by 0.11 PPL for LLaMA-1B in (He et al., 2025)

Reference 38

Resolution: verified exact; arxiv_id, observed 2026-05-25T06:55:26.362809Z

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Observation 5706d5c7-cc93-4ede-bfe2-183eaa710c76 · outbound

This paper cites We run all the experiments on one NVIDIA RTX PRO 6000 Blackwell.

HTMuon: Improving Muon via Heavy-Tailed Spectral Correction We run all the experiments on one NVIDIA RTX PRO 6000 Blackwell

Reference 39

Resolution: verified exact; arxiv_id, observed 2026-05-25T06:55:26.354579Z

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Observation e0210f5a-0d01-4626-867e-0bd34a91746e · outbound

This paper cites We put the implementations in Algorithm.

HTMuon: Improving Muon via Heavy-Tailed Spectral Correction We put the implementations in Algorithm

Reference 40

Resolution: verified fuzzy; raw_fallback, observed 2026-05-25T07:16:43.574890Z

Source-reported events for the cited work

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Observation 5eb257dd-9cb8-4ee9-9dc6-3a046390dd04 · outbound

This paper cites We put the implementations in Algorithm.

HTMuon: Improving Muon via Heavy-Tailed Spectral Correction We put the implementations in Algorithm

Reference 41

Resolution: verified fuzzy; raw_fallback, observed 2026-05-25T07:16:43.571713Z

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Observation c8698a58-ba8d-4770-bd16-5f54898e3cc0 · outbound

This paper cites We put the implementations in Algorithm.

HTMuon: Improving Muon via Heavy-Tailed Spectral Correction We put the implementations in Algorithm

Reference 42

Resolution: verified fuzzy; raw_fallback, observed 2026-05-25T07:16:43.578250Z

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Observation cca597e4-50da-4a8a-84a6-ecf6ce0479c6 · outbound

This paper cites We put the implementations in Algorithm.

HTMuon: Improving Muon via Heavy-Tailed Spectral Correction We put the implementations in Algorithm

Reference 43

Resolution: verified fuzzy; raw_fallback, observed 2026-05-25T07:16:43.567822Z

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Observation 8a57bcc5-390e-4477-8b73-02f8311d5f0a · outbound

This paper cites We put the implementations in Algorithm.

HTMuon: Improving Muon via Heavy-Tailed Spectral Correction We put the implementations in Algorithm

Reference 44

Resolution: verified fuzzy; raw_fallback, observed 2026-05-25T07:16:43.564364Z

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Pith citing papers

Observation 54fb3d8a-c3f3-410d-8b42-bfe3855b201e · inbound

RMNP: Row-Momentum Normalized Preconditioning for Scalable Matrix-Based Optimization cites this paper.

RMNP: Row-Momentum Normalized Preconditioning for Scalable Matrix-Based Optimization HTMuon: Improving Muon via Heavy-Tailed Spectral Correction

Reference 26

Resolution: metadata mismatch; arxiv_id, observed 2026-05-25T03:01:13.946888Z

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Observation f5132c57-8195-4e85-ba7d-f93ee79da015 · inbound

LionMuon: Alternating Spectral and Sign Descent for Efficient Training cites this paper.

LionMuon: Alternating Spectral and Sign Descent for Efficient Training HTMuon: Improving Muon via Heavy-Tailed Spectral Correction

Reference 10

Resolution: verified exact; arxiv_id, observed 2026-05-25T03:01:13.946888Z

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Observation 10eb4b9b-f25b-40c9-807e-4dbdf40f11f8 · inbound

LionMuon: Alternating Spectral and Sign Descent for Efficient Training cites this paper.

LionMuon: Alternating Spectral and Sign Descent for Efficient Training HTMuon: Improving Muon via Heavy-Tailed Spectral Correction

Reference 10

Resolution: verified exact; local_arxiv, observed 2026-06-30T18:35:00.452419Z

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Observation fc6e69e7-fbd2-4d1d-aa9b-b9141c244a84 · inbound

Convergence of Spectral Descent for Non-smooth Optimization cites this paper.

Convergence of Spectral Descent for Non-smooth Optimization HTMuon: Improving Muon via Heavy-Tailed Spectral Correction

Reference 18

Resolution: metadata mismatch; local_arxiv, observed 2026-06-29T19:33:54.023467Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-05T06:32:48.257954+00:00.

Observation cefa22e4-50d8-4296-86e8-13688c8eec43 · inbound

When Does Muon Help Agentic Reinforcement Learning? cites this paper.

When Does Muon Help Agentic Reinforcement Learning? HTMuon: Improving Muon via Heavy-Tailed Spectral Correction

Reference 13

Resolution: unresolved; no resolver link, observed 2026-08-01T21:13:39.521086Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 9a2e4e88-102b-4c41-97e4-78687ea8ba3b · inbound

When Does Muon Help Agentic Reinforcement Learning? cites this paper.

When Does Muon Help Agentic Reinforcement Learning? HTMuon: Improving Muon via Heavy-Tailed Spectral Correction

Reference 13

Resolution: unresolved; no resolver link, observed 2026-08-04T04:19:39.069342Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.